What Are the Two Possible Launch Angles for a Ball to Land 5 Meters Away?

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To determine the two possible launch angles for a ball to land 5 meters away when launched at a speed of 10 m/s, it's essential to apply the equations of motion. The problem involves finding the angle θ that affects both the horizontal and vertical components of the launch velocity. The horizontal component can be calculated using the cosine of the angle, while the vertical component uses the sine. A system of equations can be set up to equate the time taken for horizontal travel and vertical motion, allowing for the calculation of θ. Understanding how to decompose the initial velocity into its horizontal and vertical components is crucial for solving the problem effectively.
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Homework Statement


A ball is launched at a speed of 10ms-1. It lands 5m away. Find the two possible values of the angle, θ, which the initial trajectory makes with the horizontal.


Homework Equations


The equations of motion.


The Attempt at a Solution


I realize that I need to find the angle θ and then use sin(180-θ) to find the other possible angle however I do not know how to get it.
 
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Interesting problem.

What I'd do is set up a system of equations. You know that the time it takes for the ball the fall and the time it takes for the ball to travel 5 m is the same, right? So, build two position equations and solve for t, then set them equal to each other, leaving only one variable, your angle.

Keeping the angle as a variable, theta, can you come up with two functions, one for the y position and one for the x position? What should the values of these functions as a whole be for each one?

What part of the 10 m/s is horizontal? Which part of the 10 m/s is vertical?
 
What I don't understand is how to split to 10m/s into hortizontal and vertical components in order to get the time.
 
10 meters per second is the magnitude of the vector. Its the same concept as the hypotenuse of a triangle.
 
jumbo123 said:

Homework Statement


A ball is launched at a speed of 10ms-1. It lands 5m away. Find the two possible values of the angle, θ, which the initial trajectory makes with the horizontal.


Homework Equations


The equations of motion.


The Attempt at a Solution


I realize that I need to find the angle θ and then use sin(180-θ) to find the other possible angle however I do not know how to get it.

jumbo123 said:
What I don't understand is how to split to 10m/s into hortizontal and vertical components in order to get the time.

See the "Range and Height" figure at this introductory page:

http://en.wikipedia.org/wiki/Trajectory

.
 
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